Solve for $x$ and $y$ using elimination. ${2x-2y = -2}$ ${5x+2y = 30}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $7x = 28$ $\dfrac{7x}{{7}} = \dfrac{28}{{7}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {2x-2y = -2}\thinspace$ to find $y$ ${2}{(4)}{ - 2y = -2}$ $8-2y = -2$ $8{-8} - 2y = -2{-8}$ $-2y = -10$ $\dfrac{-2y}{{-2}} = \dfrac{-10}{{-2}}$ ${y = 5}$ You can also plug ${x = 4}$ into $\thinspace {5x+2y = 30}\thinspace$ and get the same answer for $y$ : ${5}{(4)}{ + 2y = 30}$ ${y = 5}$